Set

A set is a well-defined collection of unique objects, where each object is referred to as an element. These elements are enclosed within curly brackets {} when written mathematically.

For instance:

• The first five prime numbers form a set: {2, 3, 5, 7, 11}

• The types of incisors in human teeth can be represented as a set: [central incisor, lateral incisor]

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Sets are usually represented by capital letters such as A, B, C, etc.

Roster Form

In the roster form, we list all the elements of a set within curly brackets {} and separate them by commas.

For example:

• Let M be the set of molars in our teeth. We can write it as:

M = {first molar, second molar, third molar}

• Let Q be the set of quadrilaterals with at least two equal sides. We can represent it as:

Q = {square, rectangle, rhombus, parallelogram, kite, isosceles trapezium, dart}

Since we list all elements explicitly, this method is called the form of writing a set.

To indicate whether an element belongs to a set, we use the symbol ∈ (belongs to) and ∉ (does not belong to).

• If an element x is in set S, we write x ∈ S, meaning x belongs to S.

• If an element y is not in set S, we write y ∉ S, meaning y does not belong to S".

Examples:

• Since "second molar" is in the set M, we write: Second molar ∈∉ M and read it as "second molar belongs to M."

- Since "rhombus" is in the set Q**, we write:

Rhombus ∈∉ Q and read it as "rhombus belongs to Q."

- Since "square" is not in the set M, we write:

Square ∉∈ M and read it as "square does not belong to M."

In this method, we describe the set by stating a common property that all its elements satisfy, rather than listing each element.

Example 1: Multiples of 3 less than 20

• Roster Form: A = {3, 6, 9, 12, 15, 18}

• Set Builder Form: A = {x | x is a multiple of 3 and x < 20}

1. Order does not matter in Roster Form:

• The set of digits in Ramanujan's number (1729) can be written as: {1, 7, 2, 9} Any order is acceptablenot-acceptable.

2. No repetition in a set:

- When writing a set, each element appears only once.

- Example: The set of letters in the word "SCHOOL" is: {S, C, H, O, L} and nota {S, C, H, O, O, L}.

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